Finite Group Databasebeta

← Group #13167061

Character table — Group #13167061

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11112222222222444444444444444444444444444466666666666666666666666688888888889999121212121212121212121212121212121212121212121212181818181818181818183636363672727272108108108108
order12442346661212121233336666666666121212121212121212121212121288888888242424242424242424242424242424243666612121212122244242424242424242424242424242424242424242424242424246666121212128888242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ51111-11-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-11-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ61111-11-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-11-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111
χ71111-11-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-11-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-111-1-1-1-111
χ81111-11-1-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-11-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-111-1-11111-1-1
χ911-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-111-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11111-1-1-1-1i−ii−ii−ii−i1-11-1
χ1011-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-111-1-1iiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11111-1-1-1-1−ii−ii−ii−ii-11-11
χ1111-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111-1-1-1-1-111-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11111-1-1-1-1i−ii−ii−ii−i-11-11
χ1211-1-111-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11111-1-1-1-1-111-1-1−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11111-1-1-1-1−ii−ii−ii−ii1-11-1
χ1311-1-1-111-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-1-111-1-11111-1-1iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1111-1-1-1-111i−i−iii−i−ii1-1-11
χ1411-1-1-111-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-1-1-111-1-11111-1-1iiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-1111-1-1-1-111−iii−i−iii−i-111-1
χ1511-1-1-111-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111-1-11111-1-1−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1111-1-1-1-111i−i−iii−i−ii-111-1
χ1611-1-1-111-1-1111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-1-111-1-11111-1-1−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-1111-1-1-1-111−iii−i−iii−i1-1-11
χ172222222222222222222222222222222222222222220000000000000000000000002222222222-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2000000000000
χ1822222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-12200000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-12-1-1-12-1-1-1-1-2-2-2-200−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-211111111000000000000
χ1922222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-12200000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-12-1-1-12-1-1-1-1-2-2-2-200i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-211111111000000000000
χ2022222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-1222222-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ2122222-12-1-1-1-1-1-1-122-1-122-1-1-1-122-1-122-1-1-1-122-1-1-1-122-2-2-2-2-2-2-2-21111111111111111-12-1-1-12-1-1-1-12222-2-21111-2-21111-2-21111-2-2111122-1-1-1-1-1-1-1-1000000000000
χ222222-22-2-2-22-2-2222222-2-2-2-2-2-22222-2-2-2-2-2-2222222220000000000000000000000002-2-2-22-222-2-2-2-2-2-200000000000000000000000022-2-222-2-222000000000000
χ232222-2-1-211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-12200000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-1-211-1-2-1-111-2-2-2-200−i3−i3i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i32211-1-111-1-1000000000000
χ242222-2-1-211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-12200000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-1-211-1-2-1-111-2-2-2-200i3i3−i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i32211-1-111-1-1000000000000
χ252222-2-1-211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-211-1-2-1-111222222-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-1-111-1-111000000000000
χ262222-2-1-211-111-1-122-1-1-2-2111122-1-1-2-2111122-1-1-1-122-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-211-1-2-1-1112222-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-1-111-1-111000000000000
χ2722-2-222-2222-2-2-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000022222-2-2-2-2-2-2-222000000000000000000000000-22-2-2-2-22222000000000000
χ2822-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-20000000033−3−3−3−33333−3−3−3−333-12-1-1-1-21111-2-2220033−3−300−3−3330033−3−300−3−333-221111-1-1-1-1000000000000
χ2922-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-200000000−3−33333−3−3−3−33333−3−3-12-1-1-1-21111-2-22200−3−3330033−3−300−3−3330033−3−3-221111-1-1-1-1000000000000
χ3022-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-22i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii-12-1-1-1-2111122-2-22i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2-2-1-1-1-11111000000000000
χ3122-2-22-1-2-1-1-1111122-1-122-1-1-1-122-1-1-2-21111-2-21111-2-2−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i-12-1-1-1-2111122-2-2−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2-2-1-1-1-11111000000000000
χ3222-2-2-222-2-2222-2-22222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000000000000000000000002-2-2-222-2-222-2-2220000000000000000000000002-2-2-22222-2-2000000000000
χ3322-2-2-2-1211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-21111-2-20000000033−3−3−3−333−3−33333−3−3-1-211-1211-1-1-2-2220033−3−300−3−33300−3−3330033−3−32-211-1-1-1-111000000000000
χ3422-2-2-2-1211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-21111-2-200000000−3−33333−3−333−3−3−3−333-1-211-1211-1-1-2-22200−3−3330033−3−30033−3−300−3−3332-211-1-1-1-111000000000000
χ3522-2-2-2-1211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-21111-2-22i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-1-211-1211-1-122-2-22i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-22-1-11111-1-1000000000000
χ3622-2-2-2-1211-1-1-11122-1-1-2-2111122-1-122-1-1-1-1-2-21111-2-2−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-1-211-1211-1-122-2-2−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-22-1-11111-1-1000000000000
χ372-22i−2i02000-2002i−2i2222000000-2-2-2-20000002i−2i2i2i−2i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132000-202i−2i002-22i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13002-2002i−2i00000000000000
χ382-22i−2i02000-2002i−2i2222000000-2-2-2-20000002i−2i2i2i−2i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132000-202i−2i002-22i−2i000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13002-2002i−2i00000000000000
χ392-22i−2i02000-2002i−2i2222000000-2-2-2-20000002i−2i2i2i−2i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000002000-202i−2i00-22−2i2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000-2200−2i2i00000000000000
χ402-22i−2i02000-2002i−2i2222000000-2-2-2-20000002i−2i2i2i−2i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000002000-202i−2i00-22−2i2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000-2200−2i2i00000000000000
χ412-22i−2i0-10−i3i313−3−ii22-1-100−i3−i3i3i3-2-2110033−3−32i−2i−i−iii2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13-10−i3i310−ii3−32-22i−2i00−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ132ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1300-11−i3i3−ii3−3000000000000
χ422-22i−2i0-10−i3i313−3−ii22-1-100−i3−i3i3i3-2-2110033−3−32i−2i−i−iii2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13-10−i3i310−ii3−32-22i−2i00ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1300-11−i3i3−ii3−3000000000000
χ432-22i−2i0-10−i3i313−3−ii22-1-100−i3−i3i3i3-2-2110033−3−32i−2i−i−iii2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13-10−i3i310−ii3−3-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−2ζ5−2ζ132ζ5+2ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1300−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13001-1i3−i3i−i−33000000000000
χ442-22i−2i0-10−i3i313−3−ii22-1-100−i3−i3i3i3-2-2110033−3−32i−2i−i−iii2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13-10−i3i310−ii3−3-22−2i2i−2ζ7−2ζ232ζ7+2ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ232ζ5+2ζ13−2ζ5−2ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1300ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13001-1i3−i3i−i−33000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.